In: Statistics and Probability
There are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6-person committee. How many committees are possible containing at most 1 faculty member?
Number of faculty member = 5
Number of students and office staff = 4+3 = 7
Number of committees possible to be formed with 1 faculty member = 7C5 5C1 = 21 5 = 105
Number of committees possible to be formed with no faculty member = 7C6 = 7
Number of committees possible to be formed containing at most 1 faculty member = (Number of committees possible to be formed with 1 faculty member + Number of committees possible to be formed with no faculty member)
Number of committees possible to be formed containing at most 1 faculty member = (105 + 7) = 112
Answer: A. 112